Proof That 22/7 Exceeds ?: Mathematical Proof, Rational Number, Pi, Diophantine Approximation, Continued Fraction, Decimal Representation, Archimedes, 3rd century BC, Perimeter
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Описание:
High Quality Content by WIKIPEDIA articles! Proofs of the famous mathematical result that the rational number 22?7 is greater than ? date back to antiquity. What follows is a one-line modern mathematical proof that 22?7>?, requiring only elementary techniques from calculus. The purpose is not primarily to convince the reader that 22?7 is indeed bigger than ?; systematic methods of computing the value of ? exist. Unlike some elementary proofs, the calculus-based proof presented here is straightforward; its elegance results from its connections to the theory of diophantine approximations. Stephen Lucas calls this proposition "One of the more beautiful results related to approximating ?". Julian Havil ends a discussion of continued fraction approximations of ? with the result, describing it as "impossible to resist mentioning" in that context.Похожие книги
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